The copending application U.S. Ser. No. 06/460,408, filed Jan. 24, 1983, by the inventor hereof describes a multi-color offset rotary printing machine on which a plurality of blanket cylinders, of respective printing systems, each having a plate cylinder, inkers, and dampers, if needed, are positioned with respect to each other in ink liquid transferring relation. A partial image to be printed, for example in a first color, is applied to a blanket cylinder by a respective associated plate cylinder, and transferred to an adjacent contacting blanket cylinder which, additionally, receives a further partial image, for example in a different color. The now two-color image can be printed or transferred to yet another blanket cylinder which may receive a third partial image in a third color--and so on; eventually, an impression or printing cylinder engages a printing substrate against the final blanket cylinder. The last or final blanket cylinder in the series will carry a plurality of images, for example in different colors. The substrate is contacted only at the single impression line with the last blanket cylinder, so that paper of even poor quality can readily be printed with multi-color images without excessive tearing or kneading by being passed between a series of blanket cylinder-impression cylinder combinations.